5 research outputs found
Nontrivial Solutions for Time Fractional Nonlinear Schrödinger-Kirchhoff Type Equations
We study the existence of solutions for time fractional Schrödinger-Kirchhoff type equation involving left and right Liouville-Weyl fractional derivatives via variational methods
Hyers-Ulam Stability and Existence of Solutions for Nigmatullin’s Fractional Diffusion Equation
We discuss stability of time-fractional order heat conduction equations and prove the Hyers-Ulam and generalized Hyers-Ulam-Rassias stability of time-fractional order heat conduction equations via fractional Green function involving Wright function. In addition, an interesting existence result for solution is given
Positive solutions for Hadamard-type fractional differential equations with nonlocal conditions on an infinite interval
The purpose of this paper is to analyse the local existence and uniqueness of positive solutions for a Hadamard-type fractional differential equation with nonlocal boundary conditions on an infinite interval. The technique used to arrive our results depends on two fixed point theorems of a sum operator in partial ordering Banach spaces. The local existence and uniqueness of positive solution is given, and we can make iterative sequences to approximate the unique positive solution. For the illustration of the main results, we list two concrete examples in the last section
Nonexistence of invariant manifolds in fractional order dynamical systems
Invariant manifolds are important sets arising in the stability theory of
dynamical systems. In this article, we take a brief review of invariant sets.
We provide some results regarding the existence of invariant lines and
parabolas in planar polynomial systems. We provide the conditions for the
invariance of linear subspaces in fractional order systems. Further, we provide
an important result showing the nonexistence of invariant manifolds (other than
linear subspaces) in fractional order systems.Comment: 27 pages, 15 figure
Analysis of a Class of Fractional Nonlinear Multidelay Differential Systems
We address existence and Ulam-Hyers and Ulam-Hyers-Mittag-Leffler stability of fractional nonlinear multiple time-delays systems with respect to two parameters’ weighted norm, which provides a foundation to study iterative learning control problem for this system. Secondly, we design PID-type learning laws to generate sequences of output trajectories to tracking the desired trajectory. Two numerical examples are used to illustrate the theoretical results